Conventional lenses, such as glass optical lenses, have curved surfaces. The combination of an index difference across an interface and the curvature of the interface allows refraction and focusing to be achieved. Conventional lenses with curved boundaries can provide conversion between diverging, planar, and converging electromagnetic and light waves. This manipulation of wave propagation is achieved by the careful choice of lens material and of the geometrical interface between air and the lens material. By designing the air-lens interface in properly chosen convex, planar, and concave shapes, the direction of wave propagation can be manipulated.